What determines the magnitude of a moment (torque) about a pivot?

• A. The velocity of the moving body.
• B. The product of the force and the lever arm length.
• C. The energy stored in the system.
• D. The rate of change of momentum.

Answer: (B)

Torque about a pivot comes from how hard you push and how far from the pivot you push it, with the direction of the push relative to the lever arm mattering too. The turning effect is quantified by τ = r × F, so the magnitude is τ = r F sin(phi), where r is the distance from the pivot to where the force is applied and phi is the angle between the force and the lever arm. When the force is perpendicular to the lever arm, sin(phi) = 1 and torque is simply F times r—the strongest turning effect for that r. If the force is along the lever arm, sin(phi) = 0 and there’s no torque.

The other ideas—velocity, stored energy, or the rate of change of linear momentum—do not determine how much turning effect you get about a pivot.